Wigner's little group as a gauge generator in linearized gravity theories
Abstract
We show that the translational subgroup of Wigner's little group for massless particles in 3 + 1 dimensions generates gauge transformation in linearized Einstein gravity. Similarly, a suitable representation of the onedimensional translational group T(1) is shown to generate gauge transformation in the linearized EinsteinChernSimons theory in 2 + 1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3 + 1 and 2 + 1 dimensions. Finally, the polarization tensor of the EinsteinPauliFierz theory in 2 + 1 dimensions is shown to split into the polarization tensors of a pair of EinsteinChernSimons theories with opposite helicities suggesting a doublet structure for the EinsteinPauliFierz theory.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 August 2002
 DOI:
 10.1088/02649381/19/16/315
 arXiv:
 arXiv:hepth/0205018
 Bibcode:
 2002CQGra..19.4445S
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 Latex, 22 pages, no figures, To appear in Class. Quant. Grav